简介:
如图,梯形ABCD中,AD∥BC,∠D=90°,以AB为直径的⊙O与CD相切于E,与BC相交于F,若AB=4,AD=1,则图中两阴影部分面积之和为().
如图,梯形ABCD中,AD∥BC,∠D=90°,以AB为直径的⊙O与CD相切于E,与BC相交于F,若AB=4,AD=1,则图中两阴影部分面积之和为().
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304357360.png)
解:
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304413928.png)
解:连接OE,作AG⊥OE于点G.
由已知可知,OA=2,AD=1,OE=2,
∴OG=1,
∴AG=
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304433009.png)
,∠AOE=60°,
∵梯形中阴影面积=(2+1)×
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304453745.png)
÷2-
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304471211.png)
=
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304494902.png)
-
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304509973.png)
;
小弓形阴影面积=
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304527284.png)
-2×
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304547933.png)
÷2=
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304561155.png)
-
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304587849.png)
,
∴两阴影部分相加=
![如图,梯形ABCD中,AD∥BC,∠D=90°.](http://img2.7wenta.com/upload/wti/20140427/13986141304605213.png)
.
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